The characteristics of incandescent lamps mean that when they fail they can easily trip a 6A breaker, and therefore the designer may elect to use a fuse as the protective device.
The reason lamps can take excessive current when they "blow" is due to vaporised metal from the arc as the filament breaks creating a brief plasma flow which can be almost a dead short.
The change in resistance of a lamp filament as it heats up is essential in partially self regulating the current in the lamp. Some "lamps" known as barristers (old technology ) are designed to control the current to a certain level even when there are wide changes of voltage. Were once used to regulate current in telephones to compensate for long and short lines to the exchange,
More to the point, the inrush current of a cold filament can be 12 - 20 times the normal running current when the lamp is hot. Having said that the change of temperature of a lamp filament between the off and on condition is many times greater than that of the immersion heater in the original question.
Radiant heaters often have a significant inrush for several seconds, but nowhere near as high as a filament lamp.
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